1. Field of the Invention
The present invention relates generally to lithographic production of microelectronic circuits or other features and, more particularly, to a method for simulating an image of a patterned object formed in a polychromatic lithographic projection system.
2. Description of Related Art
Simulation of lithography of microelectronic circuits and other features is increasing in importance as modern exposure and metrology tools increase in cost, and integrated circuit (IC) feature sizes drop well below the wavelength of light. The accurate simulation of lithographic processes can be used to eliminate many experiments, and there is huge cost incentive to do this whenever possible. Sub-100 nm features represent a significant challenge in the manufacture of ICs since such feature sizes approach the resolution limits of the lithographic imaging tools employed in IC fabrication. The practical difficulty as feature sizes shrink well below half the wavelength of light (λ/2) is not in avoiding a hard resolution limit, but rather in successfully printing the circuit patterns within an acceptable tolerance about the correct dimensions even as the exposing image departs substantially from an ideal binary pattern.
One technique adopted in the semiconductor industry to meet this challenge is model-based optical proximity correction (MB-OPC, or OPC for short), in which mask shapes are pre-distorted on the basis of process simulations in order that their dimensions, as printed on the wafer, achieve target values. Lithographic simulation becomes an explicit component of the manufacturing process when OPC is used. In recent years, the use of OPC software has increased dramatically, and is now vital to modern IC chip production. Unfortunately, the models used within this OPC software are difficult to adjust to actual processes because they contain many adjustable fitting parameters, and these parameters do not correspond to measurable physical quantities. The OPC modeling software is frequently not accurate, and is too slow. One specific aspect which has not been included in OPC software is the focus blur due to laser spectral bandwidth.
The ability to accurately simulate the lithographic exposure process, including the image projection and resist expose/develop steps, has wider importance beyond OPC. Narrow process margins make it necessary to optimize as many variables as possible during lithographic printing, and this optimization cannot be accomplished by trial-and-error or heuristic rules due to the complexity involved. The high cost of test masks and metrology for complex patterns makes accurate simulation particularly desirable.
An important additional challenge arises when simulation is carried out for OPC, due to the enormous number of image calculations that OPC programs must carry out to correct the roughly 1 E8 features in state-of-the-art circuit masks. Every adjustment of each individual feature requires that multiple intensity calculations be made in order to characterize the image in a finite neighborhood around the feature. In addition, these adjustments must usually be iterated in order to accommodate the interaction of each adjusted feature with its neighbors. Practical OPC is thus highly dependent on the ability to accurately simulate the behavior of the imaging system with great rapidity. Unfortunately, known methods for simulating the effect of finite source bandwidth in imaging systems are far too slow to be practical for OPC.
Earlier generations of lithography lenses were manufactured to much more relaxed tolerances than is currently acceptable, and by those standards such lenses usually achieved acceptably good chromatic correction over the full range of wavelengths present in the source. In this context fast simulation methods were developed based on the approximation of monochromatic imaging, making it possible to calculate optical intensities with a speed adequate for OPC so long as chromatic aberration could be neglected. For example, IC masks usually contain many blocks or cells of patterns that are replicated at multiple points within the exposure field, and this design hierarchy allows a set of OPC adjustments that have been computed for a given cell to be redeployed many times without significant additional computation.
Also, IC mask patterns are polygonal in shape, and the corner angles in these polygons are almost always restricted to a very limited set of specific values. For example, most mask features are so-called “Manhattan” polygons, in which all corner angles are 90°, and this limited set of corner possibilities allows OPC software to represent any mask polygon as a superposition of pre-analyzed corners. Though the imaging process is nonlinear, it can be represented as a quadratic superposition of linear steps, with each linear step taking the form of a convolution of the mask pattern with a particular kernel. If each polygon is represented as a superposition of corners, one can then carry out these polygon convolutions very rapidly once the convolution of each possible constituent corner and kernel has been pre-calculated and stored.
The photoresist on which the image is projected in a lithographic process responds to the square of the electric field, so the imaging process is inherently nonlinear; however the squaring operation entails little computational burden. More significantly, image formation is partially coherent in practical systems, and this substantially increases the computational burden during OPC. In a purely coherent system, the electric field at some given image point (conjugate to a particular mask point) can be calculated as a 2D convolution of field contributions from nearby mask points, with the convolution kernel involved being the amplitude response function of the lens. Likewise, a 2D convolution of intensity contributions will suffice to model a system that is effectively incoherent. However, partially coherent imaging is governed by a 4D bilinear amplitude convolution, in which the field contributed from each neighboring mask point will partially interfere with the field contributed by every other neighboring mask point to a degree determined by the separation between each such pair of neighboring points. This pairwise two-fold integration over the domain of a 2D mask requires a 4D integration.
For this reason partial coherence has significant speed implications for the elementary OPC operation of calculating intensity at a given point. If feature interactions within a region of width of, for example, 20 times the lens resolution are considered significant when calculating intensity (i.e. intensity at the center of the region), then an integration in 4D will entail a 400-fold increase in computation time over a simple 2D integration.
However, using the prior art Sum of Coherent Systems (SOCS) method, it is possible to adequately approximate the 4D integral as a truncated sum of 2D integrals, each of which is evaluated using the polygon convolution method described above. Typically about 10 2D integrals are employed in this sum, entailing roughly a 10-fold increase in computation over the 2D cases of purely coherent or purely incoherent imaging. This is considered acceptable for OPC, unlike the ˜400-fold increase from direct 4D integration. The SOCS method thus makes it feasible to carry out OPC with imaging configurations that employ partially coherent illumination.
Unfortunately, an additional severe computational burden is imposed by adding the weighted contributions from many monochromatic exposures within the source spectrum to carry out an elementary intensity calculation in the polychromatic case. For example, if the source spectrum is approximated by its intensity at 20 grid points within the spectral bandwidth, then computation time increases 20-fold over the monochromatic partially coherent case when this prior-art polychromatic algorithm is used. Such an increase makes OPC completely impractical in almost all cases. While the increase can be cut in half when the spectrum and lens response are symmetrical about the center wavelength, considerably larger improvements are needed for practical usability.
In current lithographic simulations, the effect of chromatic aberration cannot be ignored, and an effective method to simulate imaging with polychromatic radiation is needed. The primary type of chromatic aberration introduces different defocus that varies linearly with the wavelength difference from the central wavelength of the spectrum. As a result, there is a net focus blurring of the final image. Other higher order aberration can be induced, depending on the detailed lens prescription. These kinds of imaging defects degrade process window, including depth of focus and exposure latitude of the imaging process. Besides the change in process window, the resulting focus blurring cause change in the optical proximity effect on imaging. This sensitivity of critical dimension (CD) to bandwidth reinforces the importance of modeling polychromatic imaging in real cases. In current lithography, a variability in CD of even 1 nm is significant, and a variability as large as 5 nm is often completely unacceptable.
Besides image quality degradation, chromatic aberration also introduces a variation in lateral magnification for each wavelength. When the center wavelength drifts a net magnification error is induced, which is considered a non-correctable error. All microlithography lasers have a finite bandwidth and are not unique from generation to generation, and from model to model. For accurate OPC with current ArF lithography lenses, it would be desirable to take chromatic aberration into account during image calculations, without incurring a significant penalty in execution time.